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AuthorTopic: can someone please explain this to me.  (Read 1362 times) Tweet Share

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mozart

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can someone please explain this to me.
« on: December 30, 2007, 11:15:53 pm »
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this concern the area which deals with the intensity of illumination
Q. A 60 W lamp produces an intesnity of illuminations of 20 units on a screen at a distance of 1.5m from the source. What will the intensity of illumination on the screen be when it is moved to 2.4 m from the source?

using this formuale: I (inversly proportional) 1/r^2

i mean how does that fit in with this problem?

And also this question reflection of light on a mirror.

Q. A girl has two mirrors on adjacent walls in her bedroom so that the mirrors meet in the corner. When she stands in front of the mmirror she can see three images of herself. Explain how these three images are formed.
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Collin Li

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Re: can someone please explain this to me.
« Reply #1 on: December 30, 2007, 11:22:01 pm »
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For the first problem, you use the inverse square law like this:

$I = \frac{k}{r^2} \Rightarrow I\cdot r^2 = k$

Yielding the formula:
$\Rightarrow I_1\cdot (r_1)^2 = I_2\cdot (r_2)^2$

Subbing in the appropriate values, you get:
$20\cdot (1.5)^2 = I_2\cdot (2.4)^2 \Rightarrow I_2 = 7.8125 \mbox{ units}$

I can't help you with the second question, I'm horrible at light, but I am pretty sure that these mirrors could not possibly be at 90 degrees to each other (should be acute angle, assuming flat walls/mirrors).
« Last Edit: December 30, 2007, 11:24:45 pm by coblin »

mozart

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Re: can someone please explain this to me.
« Reply #2 on: December 30, 2007, 11:35:02 pm »
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see where you have

I^1 . (r^1)^2 = I^2 . (r2)^2

how do you get that from the intial equation after using the inverse law.

I . r^2 = k to I^1 . (r^1)^2 = I^2 . (r2)^2

can you Please exPlain and also whats the dot mean. Is that just showing the sePeration of the two numbers?
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Mao

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Re: can someone please explain this to me.
« Reply #3 on: December 30, 2007, 11:41:52 pm »
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"$\cdot$" means multiply, the same thing as "$\times$"

$I_1\cdot (r_1)^2 = I_2\cdot (r_2)^2$ is obtained from $I = \frac{k}{r^2}$:
rearranging equation:
$k=I\cdot (r)^2$
as $k$ is constant
$k=I_1\cdot (r_1)^2$ and $k= I_2\cdot (r_2)^2$
therefore
$\Rightarrow I_1\cdot (r_1)^2 = I_2\cdot (r_2)^2$
« Last Edit: December 30, 2007, 11:46:08 pm by Obsolete Chaos »
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Collin Li

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Re: can someone please explain this to me.
« Reply #4 on: December 30, 2007, 11:42:15 pm »
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The dot just means multiply, pretty much.

The explanation of how I got to the first line to the second line isn't very simple, but I'll just try a mathematical approach:

If you have $I\cdot r^2 = k$, then you can say: $I_1\cdot (r_1)^2 = k$. You can also say: $I_2\cdot (r_2)^2 = k$. Equate them together to get $I_1\cdot (r_1)^2 = k = I_2\cdot (r_2)^2$ as required.

In chemistry, it is like how you have $c_1\cdot V_1 = c_2\cdot V_2$ coming from $n = cV$, if you have done that already.

mozart

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Re: can someone please explain this to me.
« Reply #5 on: December 30, 2007, 11:48:21 pm »
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but doesn't the ^2 when put on the I and r change the equation?
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Collin Li

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Re: can someone please explain this to me.
« Reply #6 on: December 30, 2007, 11:58:35 pm »
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I'm not sure what you mean.

mozart

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Re: can someone please explain this to me.
« Reply #7 on: December 31, 2007, 12:12:53 am »
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because you said "put them together and you get
I . r^2 = k to I^1 . (r^1)^2 = I^2 . (r2)^2 " and by putting the ^2 in front of the second part of this equation which is I^2 . (r2)^2 , wouldn't it change the equation because your putting the ^2 there. If i'm not explaining it clearly, this is what i mean.

If you use the inverse law you'd get k = I . r^2
but how did you end up with adding the extra bit to this equation I^2 . (r^2)^2
why would you add it anyway?

sorry for the hassle
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Collin Li

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Re: can someone please explain this to me.
« Reply #8 on: December 31, 2007, 02:01:31 am »
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I see what you mean. It's actually okay to do that, because $I_1$ just means intensity under one set of conditions (depends on $r_1$), while $I_2$ means intensity under another set of conditions (depends on $r_2$).

Oh, you can actually do it this way (might be easier to understand):

$I\cdot r^2 = k$

Substitute in: $I = 20$ and $r = 1.5$

$\Rightarrow k = 45$

$\Rightarrow I\cdot r^2 = 45$

Now, using that equation, substitute $r = 2.4$, and solve for $I$

This is exactly the same as what I was doing before, except I was doing it in algebra so it may have been confusing, especially with all the subscripts (like $x_1$) and superscripts (like $x^1$).

You were confusing me with your "^2", it should be "_2" to signify the subscript.
Superscript: $x^2$ (notation: x^2)
Subscript: $x_2$ (notation: x_2)
« Last Edit: December 31, 2007, 02:12:25 am by coblin »

cara.mel

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Re: can someone please explain this to me.
« Reply #9 on: December 31, 2007, 10:10:55 am »
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The mirror one is possible at right angles. You'd get the 2 images you'd expect from looking into one mirror only, and another one at the corner where they join.

How to explain it I don't remember. I was trying to draw it out but got stuck xD. It has something to do with another image being formed from the reflected images. Because they're at right angles, they'll overlap each other and you'll only get 1 more image

Like this lovely drawing:

If they were at acute angles you'd get more

In my frustration I googled it.
http://www.physicsclassroom.com/Class/refln/U13L2f.html
Look at the picture with the 2 red 2 blue and green dots in it. Each set beyond the red one is formed by the image 'reflecting' off the other mirror, obeying all the rules you already know (perpendicular to it etc). They don't explain it very well (and their right angle mirror explanation on the other page I don't really get either xD) so say if you want me to explain it further, I just think it makes more sense seeing mirrors not at 90º, and then applying it back to the 90º situation

mozart

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Re: can someone please explain this to me.
« Reply #10 on: December 31, 2007, 01:54:52 pm »
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ohhhhh yer i get you now coblin thanx yer i get mistaken by the ^2 and the _2 sorry.

Yer cara.mel that looks rioght because one image is reflected of straight, one of the other image using the i=r and another reflection on the other image using i=r. Makes sense now thanx ppl.
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Mao

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Re: can someone please explain this to me.
« Reply #11 on: December 31, 2007, 04:53:51 pm »
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ohhhhh yer i get you now coblin thanx yer i get mistaken by the ^2 and the _2 sorry.

Yer cara.mel that looks rioght because one image is reflected of straight, one of the other image using the i=r and another reflection on the other image using i=r. Makes sense now thanx ppl.
um.... all reflections obey the rule $i=r$... the two [']s are reflections of the object (you), and the [2](s) are the reflections of the reflections, but because of construction of the mirros ($90^o$), the two "re-reflections" comepletely overlap each other and hence you only observe it as one reflection
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mozart

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Re: can someone please explain this to me.
« Reply #12 on: January 01, 2008, 06:25:33 pm »
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i can understand why the two reflections occur which are the (') but that number 2 reflection is a bit confusing. How ndoes it reflect off the two images and the object? is there a drawing or somthing to show the movement of the light reflecting?
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Mao

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Re: can someone please explain this to me.
« Reply #13 on: January 01, 2008, 08:31:42 pm »
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sorry its not done with a ruler.. xD
« Last Edit: January 01, 2008, 08:45:27 pm by Obsolete Chaos »
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mozart

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Re: can someone please explain this to me.
« Reply #14 on: January 01, 2008, 08:36:24 pm »
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loolllll ur Pik actually is actually quite clear yer now it's all coming together. now i can answer the question thnx to al ur helP.

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